Explaining Thevenin Equivalent?

[Chandasouk]

http://img69.imageshack.us/i/circuitf.jpg/

Can someone explain what was done to go from Figure 4 to Fig 5? I tried source transformations but I cannot simplify it to that.

 

[pirateman99]

Thevenin Equivalent breaks any circuit into one voltage source and one resistor.

You get the 2ohm resistance on the right because you calculated the equivalent resistance in Figure 4 by removing the current source and acting like the voltage source is just a straight wire.

This will give you the two 2ohm resistors in parallel which gives you 1ohm, then that is now in series with the other 1ohm resistor giving you 2 ohms.

VTh is the Thevenin voltage and can be calculated by doing nodal analysis at node a and node b to calculated the voltage through each node.

at a 2A=Va/1ohm and at b (Vb/2)=((6-Vb)/2) giving you Va=2V and Vb=3V and since you want the Thevenin voltage across a and b, VTh = Vb-Va which gives you VTh = 3-1 or VTh = 1V

 

[Chandasouk]

Thanks. I was over complicating the method to getting the voltage source. Forgot all about node method.